\section{Goals and Outcomes}

% GOAL PARAGRAPH
I develop autonomous hybrid control systems with mathematical guarantees of safe and correct behavior.

% INTRODUCTORY PARAGRAPH Hook
Nuclear power plants require the highest levels of control system reliability. Control system failures risk economic losses, service interruptions, or radiological release.
% Known information
Nuclear plants today depend on human operators with extensive training. These operators follow detailed written procedures and strict regulatory requirements, switching between control modes based on plant conditions and procedural guidance.
% Gap
This reliance on human operators prevents autonomous control. It creates a fundamental economic challenge for next-generation reactor designs. Small modular reactors face per-megawatt staffing costs far exceeding those of conventional plants, threatening economic viability. Autonomous control systems could manage complex operational sequences without constant human supervision—but only with assurance equal to or exceeding that of human operators.

% APPROACH PARAGRAPH Solution
I produce hybrid control systems correct by construction, unifying formal methods with control theory.
% Rationale
Human operators already work this way: discrete logic switches between continuous control modes. Formal methods generate provably correct switching logic from written requirements but cannot handle continuous dynamics governing transitions. Control theory verifies continuous behavior but cannot prove discrete switching correctness. End-to-end correctness requires both approaches working together.
% Hypothesis
Two steps close this gap. First, discrete mode transitions synthesize directly from written operating procedures. Second, continuous behavior between transitions verifies against discrete requirements. This approach formalizes operating procedures into logical specifications that constrain continuous dynamics. The result: autonomous controllers provably free from design defects. 

The University of Pittsburgh Cyber Energy Center provides access to industry collaboration and Emerson control hardware, ensuring solutions align with practical implementation requirements.

% OUTCOMES PARAGRAPHS
If successful, this approach produces three concrete outcomes:

\begin{enumerate}

  % OUTCOME 1 Title
  \item \textbf{Translate written procedures into verified control logic.}
    % Strategy
    A methodology converts existing written operating procedures into formal
    specifications. Reactive synthesis tools then automatically generate
    discrete control logic from these specifications. Structured intermediate
    representations bridge natural language procedures and mathematical logic.
    % Outcome
    Control system engineers generate verified mode-switching controllers
    directly from regulatory procedures without formal methods expertise,
    lowering the barrier to high-assurance control systems.

    % OUTCOME 2 Title
  \item \textbf{Verify continuous control behavior across mode transitions.}
    % Strategy
    Methods for analyzing continuous control modes verify they satisfy
    discrete transition requirements. Classical control theory handles linear
    systems. Reachability analysis handles nonlinear dynamics. Both verify that
    each continuous mode reaches its intended transitions safely.
    % Outcome
    Engineers design continuous controllers using standard practices. Formal correctness guarantees remain intact. Mode transitions occur safely and at the correct times—provably.

    % OUTCOME 3  Title
  \item \textbf{Demonstrate autonomous reactor startup control with safety
    guarantees.}
    % Strategy
    This methodology applies to autonomous nuclear reactor startup procedures,
    demonstrating on a small modular reactor simulation using industry-standard
    control hardware. The demonstration proves correctness across multiple
    coordinated control modes from cold shutdown through criticality to power operation.
    % Outcome
    Autonomous hybrid control becomes realizable in the nuclear industry with
    current equipment, establishing a path toward reduced operator staffing
    while maintaining safety.

\end{enumerate}

% IMPACT PARAGRAPH Innovation
These three outcomes—procedure translation, continuous verification, and hardware demonstration—establish a complete methodology from regulatory documents to deployed systems.

\textbf{What makes this research new?} No existing methodology achieves end-to-end correctness guarantees for hybrid systems. This work unifies discrete synthesis with continuous verification. The key innovation: discrete specifications become contracts that continuous controllers must satisfy. Each layer verifies independently while guaranteeing correct composition. Formal methods verify discrete logic. Control theory verifies continuous dynamics. Section 2 examines why prior work fails at this integration. Section 3 details how this approach succeeds.

% Outcome Impact
If successful, control engineers create autonomous controllers from
existing procedures with mathematical proofs of correct behavior. High-assurance
autonomous control becomes practical for safety-critical applications.
% Impact/Pay-off
This capability is essential for the economic viability of next-generation
nuclear power. Small modular reactors offer a promising solution to growing
energy demands. Their success depends on reducing per-megawatt operating
costs through increased autonomy. My research provides the tools to
achieve that autonomy while maintaining the exceptional safety record the
nuclear industry requires.

These three outcomes establish a complete methodology from regulatory documents to deployed systems. 

This proposal follows the Heilmeier Catechism. Each section explicitly answers its assigned questions:
\begin{itemize}
  \item \textbf{Section 2 (State of the Art):} What has been done? What are the limits of current practice?
  \item \textbf{Section 3 (Research Approach):} What is new? Why will it succeed?
  \item \textbf{Section 4 (Metrics for Success):} How do we measure success?
  \item \textbf{Section 5 (Risks and Contingencies):} What could prevent success?
  \item \textbf{Section 6 (Broader Impacts):} Who cares? Why now? What difference will it make?
  \item \textbf{Section 8 (Schedule):} How long will it take?
\end{itemize}
Each section begins by stating its Heilmeier questions. Each section ends by summarizing its answers. This structure ensures both local clarity and global coherence.
